Despite the fact that this debate has been on the list since long before I showed up, I really think we're making progress.
I wrote and Blake responded >>A beats B, 70% winning votes (25% losing) >>B beats C, 52% winning votes (45% losing) >>C beats A, 50% winning votes (40% losing) >> >>By virtue of a slight perturbation (the sort that would fall within >>polling error margins in the real-world, nonzero-information case) >>candidate A now wins the election. In this case, if I (any many others >>like me) randomly vote B over C, we change nothing, while if I (any many >>others like me) randomly vote C over B, we may turn B's victory over C >>into a defeat, and we turn C into a Condorcet winner. This causes the >>defeat of A, our favorite. >When I talk about randomly filling out a ballot, it is something each >person would do individually. The whole group wouldn't decide to vote B >over C or C over B en masse. Now I understand what you meant by saying >this would require co-ordination. That's not what I meant when I said that (in an earlier message). What I meant was that I doubt most voters will take to the idea of random ballot completion on their own, so a faction's leaders would have to encourage their voters to do so. Even if folks decide independently to randomly complete, some voters may have some inclination to cast the vote for the candidate they prefer ever-so-slightly between those bottom two. So co-ordination from the top (random voting schemes based on the last digit of your phone number, for example) would probably be called for to guarantee a faction doesn't lean their "random" ballot completion one way, and hurt its chances. But this is not really what the above example is about. The above example simply shows that random ballot completion CAN hurt you, if you pick the wrong side. There's no denying that. But your point is well taken: if a large group of like-minded voters commit to voting truly randomly on the bottom of their ballot, then there is only a tiny chance that they will end up hurting their cause (only if their randomness ends up accidentally favoring one candidate), and they can help their cause in certain situations. So this is an advantage of margins over winning votes. The first and only one that has been demonstrated to me. I have several responses to this weakness. First, allow me to borrow from your favorite counter argument from when I was criticizing margins methods earlier on this thread. While this random ballot completion can help a faction, all they are really doing is strategic order-reversal on half the ballots, while the bottom listings on the other half of the ballots don't change anything. Needless to say, this means that you can do the same thing with order-reversal (or order fabrication, as it were) as you can with random ballots. The only time the random-ballot completion is actually the optimal approach is in the zero-information case, which of course is pretty rare in public elections. The strategic truncation issues that can cause problems in margins methods have the same property, but this still bears mentioning. Secondly, this tactic only works when one faction is aware that random ballot completion is a good plan, while the other faction is not. If everyone randomly completes, then you have exactly the same results you would have if margins methods had been used. Presumably, when it matters, all faction leaders will so advise their voters. So in the realistic zero-information case (if that's not an oxymoron) winning votes and margins will produce about the same results. Third, this failure caused by winning votes random ballot completion has an analogy in margins voting with strategic truncation. Take the case 9 ABC 8 BCA 7 CAB 3 ACB 3 BAC 3 BCA B>C 7 A>B 5 C>A 3 If the BAC voters strategically truncate to B, then C>A jumps up to 6, and B wins the election in stead of A. Granted, this is not the zero-information case, but it shows that margins can fail for the natural circular tie with strategic truncation. In winning votes, the BAC voters would have to actually order-reverse to get what they wanted. The proper response to this strategy is for the CAB voters to bury their favorite and vote ACB, which is a more radical tactic than just truncating was. So unlike most random completion problems, the best strategic response is more radical than the truncation that forced the response. I fully realize that this same effect could have been caused by order reversal in winning votes methods (although not by random second place). But I'd argue that it's much harder to convince a faction to swap positions on their ballot than to convince them to bullet vote their favorite. Finally, and most importantly in my mind, is the situations when the weaknesses of margins and winning votes methods present themselves. The only time random ballot completion in winning votes can cause a problem, but strategic truncation in margins cannot, is when there is a cyclic tie. Strategic truncation, on the other hand, can actually cause a Condorcet winner to lose. My original example from the beginning of the tread illustrates this exact point. Since the cyclic tie is, in my opinion, a relatively unlikely event, an election method that minimizes strategy when a Condorcet winner exists is very desirable. In winning votes, only order reversal can bring down a Condorcet winner, but other, less invasive options exist in margins methods. It comes down to how you think the public will react to various strategic incentives. If you truly feel that the public will have no qualms whatsoever about any manner of strategy, and indeed that they will figure out the optimal strategy without any help from their faction leaders, then there is no real difference between margins and winning votes. Both will occasionally be perverted toward undesirable results by a faction practicing order-reversal. But in my opinion, certain strategic tactics will be more palatable to the public, and will be easier to sell. Bullet voting, or strategic truncation, seems like BY FAR the easiest one to sell. You're not asking the voters to "lie", you're merely asking them to "not tell the whole truth". I expect lots of people would see it this way. It is for this reason that I consider margins methods' strategic pitfalls to be more dangerous than those of winning votes methods. A summary: ***** The strategic options that winning votes methods allow (and margins methods do not) only come up when there are cyclic ties, generally apply equally to many factions, and tend to cancel out between factions and produce identical results to margins methods. The strategic options that margins methods allow (and winning votes methods do not) can come up when there is a Condorcet winner, generally apply asymmetrically to certain factions, and often require defensive voting changes on the part of other factions to counteract, including favorite betrayal. ****** >>The moral of the story? Losing votes do matter just as much as winning >>votes in winning votes methods. They just don't matter until they become >>winning votes. I've heard the argument here that this is too sudden and >>sharp a change, since we suddenly switch from considereing ONLY the votes >>on one side to considering ONLY the votes on the other. This is sort of >>a silly argument, since every election method has some boderline where >>all of a sudden one vote causes a completely different result. How you >>count the votes (winning votes vs. margins, for example) only decides >>where this border falls; it does not make this border any less stark. >Obviously there is going to be a sudden change between who wins. On the >other hand, such a change doesn't commit me to believing that a strong win >for A has become a strong win for B. Since winning votes gives a vote of >50 to 49 precedence over one of 49 to 4, it seems like winning votes >thinks the former is in some way more decisive, or in other words, >strong. So, we can easily argue that the method goes from strong one way >to strong the other with a change of a single vote. That's quite >different than saying merely that the winner might change because of one vote. My opinion, which you are of course free to disagree with, is that this difference only matters insofar as it determines which candidate wins the election. When we examine winning votes vs. margins, the differences are clear: winning votes encourages random ballot completion in low-information elections, while margins allows strategic truncation to accomplish reversals that require strategic order-reversal in winning votes. As I explained above, I find the problems with margins to be more problematic. The actual tabulation methods that lead to these differences are, in the final analysis, sort of irrelevant. One final thought. on 3/20 I posted a message about Approval Completed Condorcet. The idea was to use a graded ballot (ABCDEF, for example). If there was not a Condorcet winner, then the candidate with the most approval votes (A's, B's, and C's in the case of ABCDEF ballots) wins the election. In my initial analysis, this method seemed at least as good as the other Condorcet methods we like to discuss. Furthermore, it seems like it could be an easier method to pitch, since the cycle-breaker is VERY intuitive. So I guess what I'm asking is... does ACC render this whole debate meaningless? Just a thought. -Adam
